CPT invariance [1]} is a mainstay of local Lorentz invariant theories in flat space-time. The CPT theorem states that, for a Hermitian local Lorentz invariant theory, CPT is a symmetry where the discrete symmetries \(C\) , \(P\)  and \(T\)  are charge conjugation, parity and time-reversal [2]} for a system with scalar \(\phi \) , spinor \(\psi \)  and vector fields \(A_{\mu }\) . A particularly straightforward proof has been given by Luders[3]}. However, in the presence of gravity since we only have local Lorentz invariance, there is no reason for the theorem to be necessarily true and Lorentz invariance to hold. This is compounded if gravity can be quantised in some theory at the Planck scale. Space and time are likely to be granular.
